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Find the equation of the bisector of the...

Find the equation of the bisector of the obtuse angle between the lines `3x-4y+7=0` and `12 x+5y-2=0.`

A

(a) 21x + 77y - 101 = 0

B

(b) 99x - 27y + 81 = 0

C

(c) 21x - 77y + 101 = 0

D

(d) None of the above

Text Solution

Verified by Experts

The correct Answer is:
21x+77y-101=0
Firstly, make the constant terms `(c_(1), c_(2))` positive.
3x-4y+7 = 0
and -12x-5y+2=0
`therefore a_(1)a_(2) + b_(1)b_(2) = (3)(-12) + (-4)(-5)`
=-36+20=-16
Hence, "-" sign gives the obtuse bisector.
Therefore, the obtuse bisector is
`((3x-4y+7))/(sqrt((3)^(2) + (-4)^(2))) = ((-12x-5y+2))/(sqrt((-12)^(2) + (-5)^(2)))`
or 13(3x-4y+7) = -5(-12x-5y+2)
or 21x+77y-101 =0
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